Our
Foucault Pendulum

The founders of the UU Church of Odessa wanted a unique
symbol of the special regard Unitarian-Universalist have for science. So Loyd
Willis, our builder, worked with the architect to design a building with a tower
sufficient in height to house a Foucault pendulum.

As a Foucault pendulum swings
back and forth, the plane of its motion slowly precesses, i.e. changes its
orientation with respect to our building. This precession illustrates the
spinning of the earth. It also demonstrates the Coriolis acceleration, which has
a major effect on the atmospheric circulation of winds about the earth, and also
of ocean currents. These effects arise because our location on our earth is not
fixed in space, but is on the surface of a giant rotating body.

Our church building thus shows
our connection to the earth and our dedication to the search for truth. It is a
great educational site, and we hope you come to visit and observe the pendulum
and consider joining our congregation.

If our church had been built at the South Pole, our
pendulum would just swing in space while the earth rotated beneath it. The
apparent motion of the plane of the pendulum swinging is said to precess.

At
our latitude in Odessa, the pendulum illustrates that the earth is rotating, but
the precession rate is not the same as it would be at the South pole. On
the other hand, one can write equations of motion for a small mass moving with
respect to the surface of a rotating earth. You can think of the earth as a very
large ball. It isnít exactly round, but we neglect that problem at first, to
get a simple picture of what effects will arise on the surface of a large
rotating ball.

If
you write these equations of motion, you come up with an acceleration term. This
term, called the Coriolis acceleration, makes moving objects curve to the right
in the northern hemisphere, and to the left in the southern hemisphere. You can
analyze the rotation of the plane of motion of the pendulum using the Coriolis
acceleration. You will notice that the plane of motion of the pendulum rotates
very slowly to the right at our Odessa location. So the plane of the pendulum
precesses in a clockwise direction when viewed from above.

Although the Coriolis acceleration may be small, if it
has a chance to act for a long time it will have a pronounced effect. Together
with atmospheric pressure differences, the Coriolis acceleration determines the
motion of the winds about the earth. It also governs the ocean currents. As an
example, with winds curving to the right in the northern hemisphere, winds will
tend to form a system rotating counterclockwise about an area of low pressure.

You cannot see the counterclockwise rotation of the
water draining out of a bathtub, because the Coriolis acceleration has only a
very small time in which to act, so other effects, such as turbulence in the
water, swamp out any effect the Coriolis acceleration could produce.

Ocean
currents also deviate to the right in the northern hemisphere. For example, if
an ocean current flows northward along the west coast, it would try to deviate
to the right. But it canít do that because the land is in the way. What
happens then is that it piles up along the shore such that the sea level would
go steadily down as you sail away from the shore. Thus the sea level is not
constant over the earth, due to ocean currents and the Coriolis acceleration

For the mathematically inclined, the motion of a
particle with respect to a rotating earth are subject to an acceleration of
Ė2(ω x V), where ω is a vector that represents the angular velocity of the earth spinning
about its axis, and V is the velocity vector of the particle with respect
to the earth, and x represents a vector cross product according to the
right hand rule. Taking into account the negative sign, this acceleration is to
the right.

The angular
velocity of the earth is roughly 366.25 x 2π radians/(365x24x3600 sec)),
which comes out to be about 0.000073 radians/second. The magnitude of the vector
cross product ω x V
will be the magnitude of ω
times the magnitude of V
times sin(Φ) where Φ is the latitude, which for our church is about 32 deg.

So a car traveling 70 mi/hr or 102.7 ft/sec would
experience a Coriolis acceleration of 2(0.000073)(102.7)sin(32) or about 0.0079
ft/sec2. This may be compared with the gravitational acceleration of
32.17 ft/ sec2 . So the Coriolis acceleration on the car, would be
about 0.024 % of the acceleration of gravity. So the Coriolis acceleration even
of a car on a freeway would be very small.

For further information, Google Foucault
pendulum and/or visit the following web sites: